One interesting sound change in Old Latin was the change of /dw/ into /b/.

For example, bellum 'war' (from which English gets 'bellicose' and 'belligerent') was once duellom.

However, duellom did survive as an archaism, most often in poetry, and is the origin of English 'duel'.

The modern meaning of 'duel' as a fight between two parties (rather than an all-out war) is probably due to a medieval association of the word with the number two, which in Latin is duo.

Other words were affected by the change of /dw/ to /b/.

These include the common adjective bonus 'good' - in Old Latin, the word was duenos.

Duenos in fact ppears in one of the oldest Latin texts, the Duenos inscription.

Why does English have two-related words that begin with du- (dual, duo, duplicate) and with bi- (binoculars, bisexual, bifocal)?

Because of this change!

The first group get du- straight from Latin duo 'two', while bi- comes from bis 'twice', which was originally duis.